% Mizar problem: t8_msualg_7,msualg_7,283,8 
fof(t8_msualg_7,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B))))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,k11_pboole(A,B,B))))
                 => ( D = C
                   => ! [E] : 
                        ( ( v2_msualg_4(E,A,B)
                          & m1_msualg_4(E,A,B,B) )
                       => ! [F] : 
                            ( ( v2_msualg_4(F,A,B)
                              & m1_msualg_4(F,A,B,B) )
                           => ( ( r6_pboole(A,E,k6_mssubfam(A,k11_pboole(A,B,B),k5_closure2(A,k11_pboole(A,B,B),D)))
                                & r2_hidden(F,C) )
                             => r2_pboole(A,E,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_closure2,cc1_lattices,cc1_membered,cc1_mssubfam,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_closure2,cc2_lattices,cc2_membered,cc2_mssubfam,cc2_xreal_0,cc3_closure2,cc3_lattices,cc3_membered,cc3_xreal_0,cc4_closure2,cc4_lattices,cc4_membered,cc4_xreal_0,cc5_closure2,cc5_xreal_0,cc6_closure2,cc6_xreal_0,cc7_closure2,cc7_xreal_0,cc8_xreal_0,d10_setfam_1,d1_setfam_1,d2_mssubfam,d3_tarski,d5_pboole,dt_g3_lattices,dt_k11_pboole,dt_k1_closure2,dt_k1_funct_1,dt_k1_mboolean,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_closure2,dt_k2_zfmisc_1,dt_k4_closure2,dt_k5_closure2,dt_k5_mssubfam,dt_k5_msualg_5,dt_k6_closure2,dt_k6_mssubfam,dt_k6_setfam_1,dt_k8_setfam_1,dt_l1_lattices,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_closure2,dt_m1_msualg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m4_pboole,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_closure2,existence_m1_msualg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m4_pboole,fc1_msualg_7,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_closure2,fc3_lattices,fc4_closure2,fc4_subset_1,fc5_closure2,fc6_membered,fc7_mssubfam,fc8_mssubfam,fraenkel_a_4_0_closure2,fraenkel_a_4_0_msualg_7,free_g3_lattices,rc11_lattices,rc1_membered,rc1_mssubfam,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_closure2,rc2_mssubfam,rc2_subset_1,rc2_xboole_0,rc2_xreal_0,rc3_lattices,rc3_mssubfam,rc3_struct_0,rc3_xreal_0,rc4_closure2,rc4_mssubfam,rc4_xreal_0,rc5_struct_0,rc6_lattices,rc9_lattices,redefinition_k2_closure2,redefinition_k5_closure2,redefinition_k6_closure2,redefinition_k6_mssubfam,redefinition_k6_setfam_1,redefinition_m1_closure2,redefinition_m2_relset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t15_closure2,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(msualg_7,t8_msualg_7)]).

fof(abstractness_v3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ),
    file(lattices,v3_lattices),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_closure2,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_fraenkel(A) ) ),
    file(closure2,cc1_closure2),
    []).

fof(cc1_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) ) ) ) ),
    file(lattices,cc1_lattices),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
       => v1_pre_circ(B,A) ) ) ),
    file(mssubfam,cc1_mssubfam),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v2_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v1_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc2_closure2),
    []).

fof(cc2_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A) ) ) ) ),
    file(lattices,cc2_lattices),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc2_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => v1_pre_circ(C,A) ) ) ),
    file(mssubfam,cc2_mssubfam),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(cc3_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v4_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v3_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc3_closure2),
    []).

fof(cc3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v15_lattices(A) ) ) ) ),
    file(lattices,cc3_lattices),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc4_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v4_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v5_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc4_closure2),
    []).

fof(cc4_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ) ),
    file(lattices,cc4_lattices),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v5_closure2(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v1_fraenkel(C) ) ) ) ) ),
    file(closure2,cc5_closure2),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc6_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v2_closure2(C,A,B)
           => ( v1_fraenkel(C)
              & v6_closure2(C,A,B) ) ) ) ) ),
    file(closure2,cc6_closure2),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( v6_closure2(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v1_fraenkel(C) ) ) ) ) ),
    file(closure2,cc7_closure2),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

fof(d10_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    []).

fof(d1_setfam_1,axiom,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    []).

fof(d2_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k5_mssubfam(A,B,C)
              <=> ! [E] : ~ ( r2_hidden(E,A)
                    & ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E))))
                       => ~ ( F = k1_funct_1(C,E)
                            & k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F) ) ) ) ) ) ) ) ),
    file(mssubfam,d2_mssubfam),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d5_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    []).

fof(dt_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( v3_lattices(g3_lattices(A,B,C))
        & l3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(dt_k11_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k11_pboole(A,B,C),A) ) ),
    file(pboole,k11_pboole),
    []).

fof(dt_k1_closure2,axiom,(
    $true ),
    file(closure2,k1_closure2),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k1_mboolean(A,B),A) ) ),
    file(mboolean,k1_mboolean),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_subset_1(k2_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))) ) ),
    file(closure2,k2_closure2),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => m1_pboole(k4_closure2(A,B,C),A) ) ),
    file(closure2,k4_closure2),
    []).

fof(dt_k5_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => m4_pboole(k5_closure2(A,B,C),A,k1_mboolean(A,B)) ) ),
    file(closure2,k5_closure2),
    []).

fof(dt_k5_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m4_pboole(C,A,k1_mboolean(A,B)) )
     => m1_pboole(k5_mssubfam(A,B,C),A) ) ),
    file(mssubfam,k5_mssubfam),
    []).

fof(dt_k5_msualg_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_msualg_5(A,B))
        & v3_lattices(k5_msualg_5(A,B))
        & v10_lattices(k5_msualg_5(A,B))
        & l3_lattices(k5_msualg_5(A,B)) ) ) ),
    file(msualg_5,k5_msualg_5),
    []).

fof(dt_k6_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_closure2(k6_closure2(A,B),A,B)
        & v2_closure2(k6_closure2(A,B),A,B)
        & v3_closure2(k6_closure2(A,B),A,B)
        & v4_closure2(k6_closure2(A,B),A,B)
        & v5_closure2(k6_closure2(A,B),A,B)
        & v6_closure2(k6_closure2(A,B),A,B)
        & m1_subset_1(k6_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))) ) ) ),
    file(closure2,k6_closure2),
    []).

fof(dt_k6_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m4_pboole(C,A,k1_mboolean(A,B)) )
     => m4_pboole(k6_mssubfam(A,B,C),A,B) ) ),
    file(mssubfam,k6_mssubfam),
    []).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    []).

fof(dt_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_m1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ! [D] : 
          ( m1_closure2(D,A,B,C)
         => m4_pboole(D,A,B) ) ) ),
    file(closure2,m1_closure2),
    []).

fof(dt_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m1_msualg_4(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(msualg_4,m1_msualg_4),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m4_pboole),
    []).

fof(dt_u1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => ( v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u1_lattices),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => ( v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u2_lattices),
    []).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

fof(existence_m1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ? [D] : m1_closure2(D,A,B,C) ) ),
    file(closure2,m1_closure2),
    []).

fof(existence_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m1_msualg_4(D,A,B,C) ) ),
    file(msualg_4,m1_msualg_4),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) ),
    file(pboole,m4_pboole),
    []).

fof(fc1_msualg_7,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_msualg_5(A,B))
        & v3_lattices(k5_msualg_5(A,B))
        & v4_lattices(k5_msualg_5(A,B))
        & v5_lattices(k5_msualg_5(A,B))
        & v6_lattices(k5_msualg_5(A,B))
        & v7_lattices(k5_msualg_5(A,B))
        & v8_lattices(k5_msualg_5(A,B))
        & v9_lattices(k5_msualg_5(A,B))
        & v10_lattices(k5_msualg_5(A,B))
        & v13_lattices(k5_msualg_5(A,B))
        & v14_lattices(k5_msualg_5(A,B))
        & v15_lattices(k5_msualg_5(A,B)) ) ) ),
    file(msualg_7,fc1_msualg_7),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( ~ v1_xboole_0(k1_closure2(A,B))
        & v1_fraenkel(k1_closure2(A,B))
        & v1_pralg_2(k1_closure2(A,B)) ) ) ),
    file(closure2,fc2_closure2),
    []).

fof(fc3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g3_lattices(A,B,C))
        & v3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,fc3_lattices),
    []).

fof(fc4_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ( v1_relat_1(k4_closure2(A,B,C))
        & v3_relat_1(k4_closure2(A,B,C))
        & v1_funct_1(k4_closure2(A,B,C))
        & v1_pre_circ(k4_closure2(A,B,C),A) ) ) ),
    file(closure2,fc4_closure2),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ( v1_relat_1(k4_closure2(A,B,C))
        & v2_relat_1(k4_closure2(A,B,C))
        & v1_funct_1(k4_closure2(A,B,C)) ) ) ),
    file(closure2,fc5_closure2),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc7_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A)
        & v1_pre_circ(C,A)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k11_pboole(A,B,C))
        & v1_funct_1(k11_pboole(A,B,C))
        & v1_pre_circ(k11_pboole(A,B,C),A) ) ) ),
    file(mssubfam,fc7_mssubfam),
    []).

fof(fc8_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k1_mboolean(A,B))
        & v2_relat_1(k1_mboolean(A,B))
        & v1_funct_1(k1_mboolean(A,B))
        & v1_pre_circ(k1_mboolean(A,B),A) ) ) ),
    file(mssubfam,fc8_mssubfam),
    []).

fof(fraenkel_a_4_0_closure2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_pboole(C,B)
        & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) )
     => ( r2_hidden(A,a_4_0_closure2(B,C,D,E))
      <=> ? [F] : 
            ( m1_closure2(F,B,C,k2_closure2(B,C))
            & A = k1_funct_1(F,E)
            & r2_hidden(F,D) ) ) ) ),
    file(closure2,a_4_0_closure2),
    []).

fof(fraenkel_a_4_0_msualg_7,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & m1_pboole(C,B)
        & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,k11_pboole(B,C,C)))) )
     => ( r2_hidden(A,a_4_0_msualg_7(B,C,D,E))
      <=> ? [F] : 
            ( m1_closure2(F,B,k11_pboole(B,C,C),k6_closure2(B,k11_pboole(B,C,C)))
            & A = k1_funct_1(F,E)
            & r2_hidden(F,D) ) ) ) ),
    file(msualg_7,a_4_0_msualg_7),
    []).

fof(free_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] : 
          ( g3_lattices(A,B,C) = g3_lattices(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(rc11_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A)
      & v15_lattices(A) ) ),
    file(lattices,rc11_lattices),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v3_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(mssubfam,rc1_mssubfam),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
          & ~ v1_xboole_0(C)
          & v1_fraenkel(C)
          & v1_pralg_2(C) ) ) ),
    file(closure2,rc2_closure2),
    []).

fof(rc2_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(mssubfam,rc2_mssubfam),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc2_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc3_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & v3_lattices(A) ) ),
    file(lattices,rc3_lattices),
    []).

fof(rc3_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v3_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(mssubfam,rc3_mssubfam),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
          & ~ v1_xboole_0(C)
          & v1_fraenkel(C)
          & v1_pralg_2(C)
          & v1_closure2(C,A,B)
          & v2_closure2(C,A,B)
          & v3_closure2(C,A,B)
          & v4_closure2(C,A,B)
          & v5_closure2(C,A,B)
          & v6_closure2(C,A,B) ) ) ),
    file(closure2,rc4_closure2),
    []).

fof(rc4_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & v1_pre_circ(C,A) ) ) ),
    file(mssubfam,rc4_mssubfam),
    []).

fof(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A) ) ),
    file(lattices,rc6_lattices),
    []).

fof(rc9_lattices,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A) ) ),
    file(lattices,rc9_lattices),
    []).

fof(redefinition_k2_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k2_closure2(A,B) = k1_closure2(A,B) ) ),
    file(closure2,k2_closure2),
    []).

fof(redefinition_k5_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => k5_closure2(A,B,C) = k4_closure2(A,B,C) ) ),
    file(closure2,k5_closure2),
    []).

fof(redefinition_k6_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k6_closure2(A,B) = k1_closure2(A,B) ) ),
    file(closure2,k6_closure2),
    []).

fof(redefinition_k6_mssubfam,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m4_pboole(C,A,k1_mboolean(A,B)) )
     => k6_mssubfam(A,B,C) = k5_mssubfam(A,B,C) ) ),
    file(mssubfam,k6_mssubfam),
    []).

fof(redefinition_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    []).

fof(redefinition_m1_closure2,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) )
     => ! [D] : 
          ( m1_closure2(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(closure2,m1_closure2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t15_closure2,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B)))
         => ( ~ v1_xboole_0(C)
           => ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(k4_closure2(A,B,C),D) = a_4_0_closure2(A,B,C,D) ) ) ) ) ),
    file(closure2,t15_closure2),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).